GAME THEORY ANALYSIS

Game Theory Analysis



Game Theory Analysis

Definition

The game theory is a branch of mathematics with applications to economics, sociology, biology and psychology, which examines the interactions between individuals making decisions in a formalized incentive framework (games). In one game, several agents look to maximize their utility by choosing particular courses of action. The final value obtained for each individual depends on the courses of action chosen by the other individuals. Game theory is a tool that helps analyze interactive optimization problems. Game theory has many applications in the social sciences. Most of the situations studied by game theory involve conflicts of interests, strategies and pitfalls. Of particular interest are situations where people can get a better result when agents cooperate with each other and when agents try to maximize their utility only. Game theory was conceived by John von Neumann. Later, John Nash, AW Tucker and others made great contributions to game theory. (Dimand, 1996, pp.100-122)

Normal form versus extensive form games

In normal form games, players move simultaneously. If the set of strategies is discrete and finite, the game can be represented by NxM matrix. A game in extensive form specifies the complete order of movement across the direction of play, usually in a game tree. (Giocoli, 2003, pp.45-64)

NxM games

One way to two-player games, in which a player has N possible actions and the other has M possible actions. In such a game, pairs of profits or payments may be represented in an array and the game is easy to analyze. NxM games give an idea of ??how one can see the structure of a game more complex.

Results Matrix game 

The results of a matrix game represent the game result in a matrix. Suppose two persons A, and B, are playing a simple game. The game is as follows: person A has a choice of "up" or "down", while B can choose "left" or "right." The game results are represented in the array of results: (Harsanyi, 1988, pp.156-180)

Left

Right

Top

(50, 100)

(0, 50)

Down

(100, 50)

(50, 0)

Dominant strategy

A key strategy is one choice that makes the player regardless of what the other does. In the game, represented in the matrix above, the dominant strategy for A is choosing "down", while the dominant strategy for B is to choose "left." These key strategies result in dominant strategy equilibrium of the game. If each player has a dominant strategy, he or she can predict the outcome of the game.

Nash Equilibrium

The Nash equilibrium was formulated by John Nash, an American mathematician, in 1951. A pair of strategies is Nash equilibrium if the choice is optimal given A's and B and B are optimal, given that of A. The Nash equilibrium is different from the dominant strategies equilibrium in which the balance of the dominant strategies, it requires strategy to be optimal for all optimal choices of B, and vice versa. The Nash equilibrium is less restrictive than the balance of optimal strategies. A game can have more than one Nash ...